On simply laced Lie algebras and their minuscule representations | Zendy

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On simply laced Lie algebras and their minuscule representations

Author(s) -

Jacob Lurie

Publication year - 2001

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/pl00013217

Subject(s) - mathematics , lie algebra , pure mathematics , simple (philosophy) , fundamental representation , invariant (physics) , killing form , affine lie algebra , lie conformal algebra , representation of a lie group , adjoint representation of a lie algebra , algebra over a field , non associative algebra , representation theory , current algebra , mathematical physics , weight , philosophy , epistemology

. In this paper we adapt a known construction for the simply laced, semisimple Lie algebras (over Z), and thereby obtain a very simple construction for all minuscule representations of those Lie algebras (again over Z). We apply these results to give explicit formulas for tensors invariant under the exceptional algebras and .

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